Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}7x+6y &= -6 \\ 7x+8y &= 6\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $8y = -7x+6$ Divide both sides by $8$ to isolate $y$ $y = {-\dfrac{7}{8}x + \dfrac{3}{4}}$ Substitute this expression for $y$ in the first equation. $7x+6({-\dfrac{7}{8}x + \dfrac{3}{4}}) = -6$ $7x - \dfrac{21}{4}x + \dfrac{9}{2} = -6$ Simplify by combining terms, then solve for $x$ $\dfrac{7}{4}x + \dfrac{9}{2} = -6$ $\dfrac{7}{4}x = -\dfrac{21}{2}$ $x = -6$ Substitute $-6$ for $x$ back into the top equation. $7( -6)+6y = -6$ $-42+6y = -6$ $6y = 36$ $y = 6$ The solution is $\enspace x = -6, \enspace y = 6$.